From what I've heard in interviews with people who know Fred Thompson, when he takes on a role, it isn't Fred Thompson playing that character, but rather that character being played as Fred Thompson. In other words, what you see is always Fred, whether as himself or someone else. Did I make any sense with that? (I like him)
Whoever told you that about Fred, is absolutely correct.
I wasn't always happy with him as my senator, but so far looks like the best thing that we have going.